How do we speed up the disproportionation reaction of #"thiosulfate ion"# to give elemental sulfur, and sulfate anion?
The two ways to speed up sulfur disproportionation are (i) raise the temperature, or (ii) add a catalyst. Changing the concentration of reactants will also cause the speed of the reaction to change.
As you know, sulfur in thiosulfate will disproportionate under these conditions. The reaction is distinguished by the deposit of a fine white precipitate of elemental sulfur.
Any reaction rate will reasonably increase upon the increase of temperature. A reaction rate will also increase upon the addition of a catalyst. A solid metal surface (of silver?) should act as a heterogeneous catalyst.
Another way of changing the speed of a reaction like this is to change the concentration of reactants. Here is a video showing this effect...